In testing the heat resistance of electrical components, safety engineers for an appliance manufacturer routinely subject wiring connectors to a temperature of 450 degrees Fahrenheit, then record the amount of time it takes for the connector to melt and cause a short circuit. Past experience has shown the standard deviation of failure times to be 6.4 seconds.
In a simple random sample of 40 connectors from a very large production run, the mean time until failure was found to be 35.5 seconds.
Construct and interpret the 99% confidence interval for μ = the mean time until failure for all of the connectors from the production run.